1 Question:
Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins. Write and simplify an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.
Correct Answer:
m represents the number of batches of muffins. So, 10 - m represents the number of batches of bread.
Total time required = Time required to bake muffins + Time required to bake bread
Time required to bake muffins = 30m
Time required to bake bread = 50(10 - m)
The expression for the total time required to bake a combination of muffins and bread if each batch is baked separately is:
30m + 50(10 - m)
= 30m + 500 - 50m [Distribute 50] = 500 - 20m [Combine like terms]
2 Question:
Identify which expressions are equivalent for the given value of x.
(x + 3)2, (x2 + 9), (x2 + 6x + 9); x = 2 Correct Answer:
Substitute x = 2 in each expression.
(x + 3)2
= (2 + 3)2
= (5)2
= 25
(x2 + 9)
= (2)2 + 9
= 4 + 9
= 13
(x2 + 6x + 9)
= (2)2 + 6(2) + 9
= 4 + 12 + 9
= 25
For x = 2, the expressions (x + 3)2 and (x2 + 6x + 9) have the same value (25), so they are equivalent. 3Question:
Which expression is greatest when s = 10? Correct Answer:
Find the value of each expression for s = 10 and then compare.
Number of inches in s feet
1 foot = 12 inches
s feet = 12s inches
10 feet = 12 x 10 = 120 inches
Number of days in s weeks
1 week = 7 days
s weeks = 7s days
10 weeks = 7 x 10 = 70 days
Number of minutes in s hours
1 hour = 60 minutes
s hours = 60s minutes
10 hours = 60 x 10 = 600 minutes
Number of inches in s yards
1 yard = 36 inches
s yards = 36s inches
10 yards = 36 x 10 = 360 inches
Out of 120, 70, 600, and 360, the greatest is 600.
So, for s = 10, the expression ‘number of minutes in s hours’ is the greatest.
Enrique is baking muffins and bread. He wants to bake a total of 10 batches. Each batch of muffins bakes for 30 minutes, and each batch of bread bakes for 50 minutes. Let m represent the number of batches of muffins. Write and simplify an expression for the total time required to bake a combination of muffins and bread if each batch is baked separately.
Correct Answer:
m represents the number of batches of muffins. So, 10 - m represents the number of batches of bread.
Total time required = Time required to bake muffins + Time required to bake bread
Time required to bake muffins = 30m
Time required to bake bread = 50(10 - m)
The expression for the total time required to bake a combination of muffins and bread if each batch is baked separately is:
30m + 50(10 - m)
= 30m + 500 - 50m [Distribute 50]
= 500 - 20m [Combine like terms]
2 Question:
Identify which expressions are equivalent for the given value of x.
(x + 3)2, (x2 + 9), (x2 + 6x + 9); x = 2
Correct Answer:
Substitute x = 2 in each expression.
(x + 3)2
= (2 + 3)2
= (5)2
= 25
(x2 + 9)
= (2)2 + 9
= 4 + 9
= 13
(x2 + 6x + 9)
= (2)2 + 6(2) + 9
= 4 + 12 + 9
= 25
For x = 2, the expressions (x + 3)2 and (x2 + 6x + 9) have the same value (25), so they are equivalent.
3 Question:
Which expression is greatest when s = 10?
Correct Answer:
Find the value of each expression for s = 10 and then compare.
Number of inches in s feet
1 foot = 12 inches
s feet = 12s inches
10 feet = 12 x 10 = 120 inches
Number of days in s weeks
1 week = 7 days
s weeks = 7s days
10 weeks = 7 x 10 = 70 days
Number of minutes in s hours
1 hour = 60 minutes
s hours = 60s minutes
10 hours = 60 x 10 = 600 minutes
Number of inches in s yards
1 yard = 36 inches
s yards = 36s inches
10 yards = 36 x 10 = 360 inches
Out of 120, 70, 600, and 360, the greatest is 600.
So, for s = 10, the expression ‘number of minutes in s hours’ is the greatest.